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Answer :
Sure! Let's solve the problem step by step.
Jerald's height as a function of time is given by the equation:
[tex]\[ h = -16t^2 + 729 \][/tex]
We need to find the time interval when Jerald is less than 104 feet above the ground. So, we set up the inequality:
[tex]\[ -16t^2 + 729 < 104 \][/tex]
### Step 1: Solve the Inequality
1. Subtract 729 from both sides:
[tex]\[ -16t^2 < 104 - 729 \][/tex]
[tex]\[ -16t^2 < -625 \][/tex]
2. Divide each side by -16. Remember, dividing by a negative number reverses the inequality sign:
[tex]\[ t^2 > \frac{625}{16} \][/tex]
3. Calculate the square root of both sides:
[tex]\[ t > \sqrt{\frac{625}{16}} \][/tex]
[tex]\[ t > \frac{25}{4} \][/tex]
[tex]\[ t > 6.25 \][/tex]
### Conclusion
Jerald's height is less than 104 feet for values of [tex]\( t > 6.25 \)[/tex].
So, the correct time interval is:
[tex]\( t > 6.25 \)[/tex]
Jerald's height as a function of time is given by the equation:
[tex]\[ h = -16t^2 + 729 \][/tex]
We need to find the time interval when Jerald is less than 104 feet above the ground. So, we set up the inequality:
[tex]\[ -16t^2 + 729 < 104 \][/tex]
### Step 1: Solve the Inequality
1. Subtract 729 from both sides:
[tex]\[ -16t^2 < 104 - 729 \][/tex]
[tex]\[ -16t^2 < -625 \][/tex]
2. Divide each side by -16. Remember, dividing by a negative number reverses the inequality sign:
[tex]\[ t^2 > \frac{625}{16} \][/tex]
3. Calculate the square root of both sides:
[tex]\[ t > \sqrt{\frac{625}{16}} \][/tex]
[tex]\[ t > \frac{25}{4} \][/tex]
[tex]\[ t > 6.25 \][/tex]
### Conclusion
Jerald's height is less than 104 feet for values of [tex]\( t > 6.25 \)[/tex].
So, the correct time interval is:
[tex]\( t > 6.25 \)[/tex]
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